An observer, moving at a speed of 0.995c relative to a rod as shown measures its length to be 2.00m and sees its length to be oriented at 30.0 degrees with respect to the direction of motion.(adsbygoogle = window.adsbygoogle || []).push({});

a) What is the proper length of the rod? (Length as measured at rest)

b) What is the orientation angle in a reference frame moving with the rod? (Again, in rest frame)

I've found the correct values, however the math seems ambiguous. I was wondering if there was another way to solve it, with cleaner mathematics.

Do = the length of the rod as measure when the rod is moving a .995c

Lo = the adjacent side of the triangle formed by the rod moving at .995

Lo = DoCos(30.0)

D = the actual length of the rod as observed from the rest frame

L = the actual length of the adjacent side of the triangle formed by the rod in the rest frame

@ = the angle formed between L and D.

h = height of the rest frame triangle

L = Lo/sqrt(1-v^2/c^2) = DoCos(30)/sqrt{(1-(.995c)^2/c^2)}

L = 17.34m

To find D you can use the following equations.

Tan(@) = h/L

Sin(@) = h/D

Cos(@)=L/D

D^2 = L^2 + h^2

I ended up getting this to solve for D.

D = sqrt{L^2 + L^2*Sin^2{Cos^-1(L/D)}^2}

My calculator solved it and got D = 17.26m or 17.42m.

The answers are 17.3m and 3.30 degree.

Is there a cleaner way to do it?

Am I missing something?

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